FOM: Is every provable theorem capable of an elementary proof?
Robert S Tragesser
RTragesser at compuserve.com
Thu Dec 11 07:44:57 EST 1997
Subject: A foundationally/philosophically important question(is it?): Is
every provable theorem
capable of an elementary proof?
In view of Steve Simpson's remarks, I thought I should post a distinct
message to say:
I came to see that what I was trying to point toward with the
meaning/significance distinction conicides with the distinction between
elementary and nonelementary proof.
This distinction is importantly connected with meaning and
analyticity -- as suggested by Gian-Carlo Rota in INDISCRETE THOUGHTS chpt7
(Birkhauser Boston 1997), that elementary proofs somehow arise out of the
concepts involved in the theorem at issue. (Though I am open to the
suggestion that elementary proof be characterized independently of the
notion of analyticity. . .perhaps Reverse Mathematicians might argue so?)
Then I wanted to make the point that the topic of elementary proof?
is philosophically and foundationally important, as for example in the
question of whether CH might have a nonelementary (but perhaps not an
elementary) proof/disproof.
Is there a reasonable explanation of "elementary proof" that would
allow some sort of decisive answer to the question:::
Is every provable theorem capable of an elementary proof?
rbrt tragesser
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